The U(N) chiral model and exact multi-solitons

TL;DR

This paper develops a method to generate exact multisoliton solutions for the principal chiral model and its noncommutative extension, expressing solutions explicitly via quasi-determinants, advancing understanding of integrable systems.

Contribution

It introduces a binary Darboux transformation approach to obtain explicit multisoliton solutions for noncommutative principal chiral models and related gauge theories.

Findings

Exact multisoliton solutions expressed via quasi-determinants.

Extension of solutions to noncommutative (anti) self dual Yang Mills equations.

Explicit construction method for noncommutative integrable models.

Abstract

We use a binary Darboux transformation to obtain exact multisoliton solutions of the principal chiral model and its noncommutative generalization. We also show that the exact multisolitons of the noncommutative principal chiral model in two dimensions and noncommutative (anti) self dual Yang Mills equations in four dimensions can be expressed explicitly in terms of quasi-determinants.